Find the center and radius of 2x^2 + 2y^2 - 12x + 8y - 24 = 0

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For Exercises 17 And 18, Find The Acute Angle Between The Given Lines By Using Vectors Parallel To The Lines.

y = x , y = 2 x + 3

The acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.

We are given the lines:

y = x

y = 2 x + 3

The formula for finding the angles between two vectors is given by:

cos θ = u · v / | u | | v|

We know that (0,0) and (1, 1) lies on the line y = x.

Now, vector u for the line y = x will be:

u = (1,1) - (0,0) = {1, 1}

(0,3 ) and (1, 5) lies on the line y = 2 x + 3

Similarly, vector v will be equal to:

v = (1, 5) - (0, 3) = {1, 2}

cos θ = {1, 1} · {1, 2} / √1 + 1 √1 + 4

cos θ = 1 + 2 / √10

cos θ = 3 / √10

θ = cos⁻¹ ( 3 / √10)

θ = 18.4349°

Therefore, the acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.

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Answer:

yes this is correct

Step-by-step explanation:

this is correct because angle gqh is adjacent to mqk, meaning they are the same degree which would mean kqg and hqm are adjacent

The number of players the team can bring to the tournament are 15

Firstly we need to form the equation. The components of equation based on given information are as follows -

Total amount raised by softball team = Cost of bus + Cost of meal × number of players

Let the number of players be represented with x.

1943.50 = 1148.50 + 53×x

Rewriting the equation

53x = 1943.50 - 1148.50

Performing subtraction to Right Hand Side of the equation

53x = 795

Shifting 75 to Right Hand Side of the equation

x = 795 ÷ 53

Performing division at Right Hand Side of the equation

x = 15

Hence, 15 players the team can bring to the tournament.

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The hourly rate is $9.40 per hour.

It should be noted that in this case, Julio works for 44 hours which mean 15 hours more than 29 hours.

He gets 1.3 times rate for this 15 hours and normal rate for the first 29 hours. Then the salary he would get should be: 29x + 1.3x(15)= 29x + 19.5x= 48.5x

Julio gets $456.32 which was 48.5 times of his hourly rate. The hourly rate would be:

= $456.32 /48.5

= $9.40/hour

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Julio is paid 1.3 times his normal hourly rate for each hour he works over 29 hours in a week. last week he worked 44 hours and earned $456.32.

Calculate the hourly rate.

Answer:

15 minutes=1km

1 minute=?

(15m:m)×1km

minutes cancel minutes

15×1km=15km

Answer:

y = -1

Step-by-step explanation:

→ First determine which axis the line passes through

y

→ Find which point the line passes through

-1

→ Equate both variables

y = -1

Answer:

More, by 0.05 or [tex]\frac{1}{20}[/tex] inches more.

Explanation:

Find out if the amount of rain was more or less by subtracting the desired outcome from the real outcome. If the answer comes out as positive then the amount of rain was more and if the answer is negative, it was less.

Workout:

[tex]\sf real \ outcome - desired \ outcome[/tex]

[tex]3.8 - 3\dfrac{3}{4}[/tex]

[tex]3.8 - 3.75[/tex]

[tex]0.05[/tex]

Hence, The rain was more than ginny expected by 0.05 inches more.

Answer:

7% of the number is 1.

Step-by-step explanation:

21%=3

Divide both sides by 3

7%=1

Answer:

1

Step-by-step explanation:

let x be the number.so.......

if 21%of a number means 21÷100*the number(x)=3

21÷100×X=3 so when we solve this first we have to criss-cross and then 21*X=3*100

then we both divide by 21 in order to get x .so x is going to be 100 divided by 7

then.......

we are asked to get how much percent of 100÷7 is 7% so...let the answer be y

7÷100*X=y

7÷100*100*7 =Y

when calculated the answer will possibly be 1 :)))

Based on the given.

If [tex]m∠2 = 59°[/tex]

Then, [tex]m∠4 = 59 °[/tex]

(reason: vertically opposite angles are equal)

If [tex]m∠4 = 59 °[/tex]

Then, [tex]m∠1⟹ 180 - 59 = 121 °[/tex]

(reason: angles on a straight line = 180°)

If [tex]m∠1 = 121°[/tex]

Then, [tex]m∠3 = 121°[/tex]

(reason: vertically opposite angles are equal)

Therefore:

[tex]m∠1 = 121°[/tex]

[tex]m∠3 = 121°[/tex]

[tex]m∠4 = 59 °[/tex]

See attached image for the placement of the values.

Answer: a. 12x+19

b. 67

Step-by-step explanation:

a. P=a+b+c+d

P=x+7+2x+2+8x+x+10

P=x+2x+8x+x+7+2+10

P=3x+9x+19

P=12x+19

b. P=12(4)+19

P=48+19

P=67

in function notation, we get that the transformed function is:

g(x) = -2*f(x - 10) + 800

Here the parent function is:

f(x) = x^2

And the transformed function is the one graphed in the lower right side of the given image.

Notice that the y-intercept of the transformed function is y = 600.

The x-intercepts are x = -10 and x = 30

Then the polynomial is something like:

y = a*(x + 10)*(x - 30)

Using the fact that the y-intercept is y = 600, then:

600 = a*(0 + 10)*(0 - 30) = a*-300

600/-300 = a = -2

The transformed function is:

g(x) = -2*(x + 10)*(x - 30)

Expanding that:

g(x) = -2( x^2 + 10x - 30x - 300)

Completing squares we get:

g(x) = -2*(  x^2 - 20x - 300)

      = -2*(x^2 - 2*10*x - 300)

Now we can add and subtract 100, so we get:

-2*(x^2 - 2*10*x - 300 + 100 - 100)

-2*(  (x - 10)^2 - 400)

Finally, expanding that:

g(x) = -2*(x - 10)^2 + 800

Writing it in function notation, we get that the transformed function is:

g(x) = -2*f(x - 10) + 800

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The value of A + H is 25 for the given sequence.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Given that sum of any three consecutive terms is 30

Since c = 5

So a + b + c = 30

a + b = 25

⇒ (a+b)+(c+d+e)+(f+g+h)

⇒ 25 + 30 + 30 = 85

Now,

a+b+c+d+e+f+g+h = 85

a + h +(b+c+d)+(e+f+g) = 85

a + h + 30 + 30 = 85

a + h = 25

Hence "The value of A + H is 25 for the given sequence".

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Answer:
3(x - 8) < 15

Step-by-step explanation:

3(x - 8) < 15

3x - 24 < 15

3x < 39

x < 13

Answer: $25 to each friend

Step-by-step explanation: 100 divided by 4 = 25

Answer:

35 small pies

Step-by-step explanation:

  Let the number of large pies be 'l' and

        The number of small pies be 's'.

Total pies sold = 45

⇒  l + s  = 45  ------------(I)

         l = 45 - s  -------(II)

Cost of 45 pies = $120

         Cost of 1 large pie = $5

         Cost of 'l' large pies = 5*l = 5l

    Cost of 1 small pie = $2

   Cost of 's' small pie = 2*s = 2s

         5l + 2s  = 120 --------------(III)

Solving : substitution method

Substitute l = 45 -s in equation (III)

         5*(45 - s) + 2s = 120

       5*45 - 5*s + 2s = 120

        225 - 5s + 2s  = 120   {Combine like terms}

               225 - 3s   = 120

                      -3s     = 120 - 225    {Subtract 225 from both sides}

                           -3s = -105

                              s = -105 ÷ (-3)    {Divide both sides by (-3)}

                             s = 35

Substitute s = 35 in equation (II),

     l = 45 - s

       = 45 - 35

    l = 10

            [tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]

Answer:

Step-by-step explanation: well first their is int a chart but bye reading the question i think is is Beth.

i hope this helped.

Answer:5 teams

Step-by-step explanation:

The gallons of water that a clydsdale drink in 28 days will be 840 gallons.

It should be noted that Clyde's dale drinks about 120 gallons of every 4 days. Therefore, the gallons Frank in a day will be:

= 120 / 4

= 30 gallons

Therefore, the gallons drank for 28 days will be:

= 30 × 28

= 840 gallons.

Therefore, the gallons of water that a clydsdale drink in 28 days will be 840 gallons.

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The theoretical mean and standard deviation is 22 and 38 respectively

np>5 and n(1-p)>5 for normal approximation

p=0.77

np>5  n×0.77>5=6.49

n(1=0.77)>5

n>5/0.23

n=21.7

The standard error of the mean for a sample size of 153 is 25 . In quest to reduce the SE of the mean in half(to 12.5 )

Standard error of sample maean is se=sd/sqrt n

se=sd/sqrt 153

Taking four times of sample size we get 4×153=612

The required sample size is 612

The mean of an infinite population is 73 and a standard deviation of 38 . The sample size of 121 is taken randomly from the given population. The SE of the sample mean equals:

standard error of the sample mean =38/sqrt121=3.4545

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The vector u is  [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex].

The linear combination 2u + 3v + 5w  is 19/3 i + 17/3 j + 6k.

According to the given question.

v = (2, 3, 1)

w = (1, 1, 1)

And

3u + 2v + 4w = (1, 2, 3)

From,

v = (2, 3, 1)

⇒ v = 2i + 3j + 1k

w = (1, 1, 1)

⇒ w = i + j + j

a). Let vector u be xi + yj + zk

Here,

3u + 2v + 4w = (1, 2, 3)

⇒ 3u + 2v + 4w = i + 2j + 3k

⇒ 3(xi + yj + zk) + 2(2i + 3j + k) + 4(i + j +k) = i + 2j + 3k

⇒ 3xi + 3yj + 3zk + 4i + 6j + 2k + 4i + 4j + 4k = i + 2j + 3k

⇒3xi + 3yj + 3zk + 8i + 10j + 6k = i + 2j + 3k

⇒ 3xi + 3yj + 3zk  = i + 2j + 3k - 8i -10j -6k

⇒ 3xi + 3yj + 3zk = -7i -8j -3k

⇒ xi + yj + zk = (1/3)(-7i -8j-3k)

⇒ xi + yj + zk = [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex]

b). The linear combination

2u + 3v + 5w

= 2(-7/3i -8/3j - k ) + 3(2i + 3j + k) + 5(i + j + k)

= -14/3 i -16/3j -2k + 6i + 6j + 3k + 5i + 5j + 5k

= -14/3 i -16/3j -2k  + 11i + 11j + 8k

= 19/3 i + 17/3 j + 6k

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Answer:

14

Step-by-step explanation:

7/4:4 = x:32

x = 32(7/4) / 4 = 14

Answer:

The bottom Option

Note:

Due to my sus vibes from your questions, this is the last one I am answering from you. this is basic and easy if you read it.

[tex]4 \div \frac{2}{5} [/tex]

[tex]4 \times \frac{5}{2} [/tex]

[tex]2 \times 5[/tex]

[tex]10[/tex]

Answer:10

Step-by-step explanation:

first step 4× 5/2
second step 4x5
                       2

third step is to simplify 20/2 which is
10

​

the angle measures less than 90°, thus, the correct classification is acute.

First, let's define the possible angles that we have here:

Notice that the angles HML and LMK should add up to 180°, then we can write:

∠HML + ∠LMK = 180°

132° + ∠LMK = 180°

∠LMK = 180° - 132° = 48°

Now we can see that:

∠JML = ∠JMK + ∠LMK

∠JML = 41° + 48° = 89°

So the angle measures less than 90°, thus, the correct classification is acute.

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Answer:

12.17634

Step-by-step explanation:

Answer: $1,544.40

Step-by-step explanation: It just is

Answer:

4. 8.4×10^5

Step-by-step explanation:

The exponent of ×10 is the amount of places that you move the decimal. When the exponent is negative, you move the decimal to the left and when it is positive, you move it to the right. Number 1 and 2 are wrong right away because they move the decimal to the left which is not what we want. Number 3 is wrong because there are not enough 0's when we move the decimal. So, option 4 is correct. I hope this helps!

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Consumer affairs investigator records the repair cost for 10 randomly selected VCRs. A sample mean of $72.82 and standard deviation of $24.17 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Construct the 90% confidence interval. Round your answer to two decimal places.

We get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).

We are given that the number of VCRs are 10.

So, we get that:

Sample size = n = 10

Now, we get the degree of freedom as:

d o f = n - 1

d o f = 10 - 1

d o f = 9

For 90% confidence interval , critical value will be:

t (0.10, 9) = 1.833

Lower limit of 90% confidence interval will be:

Lower interval  = Mean - t (0.10,9) × s / √n

= 72.82-1.833 × 24.17 /√10

= 58.81

Upper limit of 90% confidence interval will be:

Upper interval = Mean + t (0.10,9) × s /√n

= 72.82 + 1.833 × 24.17/√10

= 86.83

Therefore, we get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).

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